922 Some geometry problems from recent journals
Crux 2823, proposed by Christopher J. Bradley, Clifton COllege,
Britol, UK
Suppose thatL,M,Nare points onBC,CA,ABrespectively, and are
distinct fromA,B,C. Suppose further that
BL
LC=
1 −λ
λ,
CM
MA
=
1 −μ
μ,
AN
NB
=
1 −ν
ν,
and that the circlesAMN,BNL, andCLMmeet at the Miquel pointP.
Find[BCP]:[CAP]:[ABP]in terms ofλ,μ,νand the side lengths
of triangleABC.